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CBSE Class 12 Mathematics 2026 Main Paper 65/2/3 · Q232 Marksparametric_derivatives

CBSE Class 12 Mathematics 2026 Main Paper 65/2/3 · Question 23 (Continuity And Differentiability)

If \(x=e^{\sin^{-1}t}\) and \(y=e^{\cos^{-1}t}\), find dy/dx at \(t=1/\sqrt2\).

✅ Step-by-Step Solution

Final Answer: −1.
  1. For |t|<1 the chain rule gives dx/dt=x/√(1−t²) and dy/dt=−y/√(1−t²).
  2. The quotient is −y/x. At t=1/√2 the inverse sine and cosine both equal π/4.
  3. Thus x=y at this parameter and dy/dx=−1.

📋 CBSE Stepwise Marking Scheme

  • [0.5 marks] For |t|<1 the chain rule gives dx/dt=x/√(1−t²) and dy/dt=−y/√(1−t²).
  • [1 mark] The quotient is −y/x. At t=1/√2 the inverse sine and cosine both equal π/4.
  • [0.5 marks] Thus x=y at this parameter and dy/dx=−1.

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